Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics

In M. Baldoni, M. Dastani, B. Liao, Y. Sakurai & R. Zalila Wenkstern (eds.), PRIMA 2019: Principles and Practice of Multi-Agent Systems. 93413 Cham, Germany: Springer. pp. 202-218 (2019)

Authors
Tim Lyon
Vienna University of Technology
Abstract
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate.
Keywords STIT  Multi-agent reasoning  Proof theory  Labelled calculi  Proof search  Decidability  Automated reasoning  Propagation rules  Logics of agency  Sequent
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References found in this work BETA

Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Complexity Results of STIT Fragments.François Schwarzentruber - 2012 - Studia Logica 100 (5):1001-1045.
Properties of Logics of Individual and Group Agency.Andreas Herzig & François Schwarzentruber - 2008 - In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7. CSLI Publications. pp. 133-149.

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